Abstract: Assume that $X$ and $Y$ are real Banach spaces with the same finite dimension. In this paper we show that if a standard coarse isometry $f:X\rightarrow Y$ satisfies an integral convergence condition or weak stability on a basis, then there exists a surjective linear isometry $U:X\rightarrow Y$ such that $\|f(x)-Ux\|=o(\|x\|)$ as $\|x\|\rightarrow\infty$. This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity. As a consequence, we also obtain a stability result for $\varepsilon$-isometries which was established by Dilworth.

Key words: coarse isometry, linear isometry, finite dimensional Banach spaces